Penalising Brownian Paths (eBook)

Bernard Roynette, Marc Yor (Autoren)

eBook Download: PDF

2009 | 2009
XIII, 275 Seiten
Springer Berlin (Verlag)
978-3-540-89699-9 (ISBN)

Infos

Penalising a process is to modify its distribution with a limiting procedure, thus defining a new process that differs from the original. This book presents a number of examples of such penalisations in the Brownian and Bessel processes framework.

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Penalising a process is to modify its distribution with a limiting procedure, thus defining a new process whose properties differ somewhat from those of the original one. We are presenting a number of examples of such penalisations in the Brownian and Bessel processes framework. The Martingale theory plays a crucial role. A general principle for penalisation emerges from these examples. In particular, it is shown in the Brownian framework that a positive sigma-finite measure takes a large class of penalisations into account.

Inhalt

Some penalisations of theWiener measure.- Feynman-Kac penalisations for Brownian motion.- Penalisations of a Bessel process with dimension d(0 d 2) by a function of the ranked lengths of its excursions.- A general principle and some questions about penalisations.

Produkt-Details

• Erscheint lt. Verlag: 31.7.2009
• Reihe/Serie: Lecture Notes in Mathematics
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: 60J65, 60F99, 60J25, 60G44, 60G30, 60J55 • Bessel process • Brownian motion • Martingale • Martingales • Penalisations • Probability Theory
• ISBN-10: 3-540-89699-6 / 3540896996
• ISBN-13: 978-3-540-89699-9 / 9783540896999